How to plot several terms in a Fourier series

[rmiller70015]

I was given a function that is periodic about 2π and I need to plot it. I was wondering if there is a way to input a value and have mathematica generate a new graph with the number of iterations. The function is:

$$\sum_{n=1}^{N}\frac{sin(nx)}{n}$$ where n is an odd integer. I guess a better way to express the function is
$$\sum_{k=0}^{N}\frac{sin((2k+1)x)}{2k+1}$$

So far I've only used mathematica to plot simple functions and solve ODE's so I'm not quite sure how to approach this.

 

[Orodruin]

Exactly what do you want to do? Do you want to update the figure (like an animation) or do you want to add additional curves to the same plot?

 

[rmiller70015]

I actually found a python source code that did what I needed, but thank you for your willingness to help.

 

[Dr Transport]

Matlab in about 10 lines...

clear all;

x=linspace(0, 3*pi, 1000);
Z = 0;
for k = 1:3
    y = sin((2*k+1)*x)/(2*k+1);
   plot(x,y)
   hold on;
   Z = Z+y;
end
plot(x,Z);
hold off;